SMILE

Stochastic Models for the Inference of Life Evolution

Presentation

SMILE is an interdisciplinary research group gathering probabilists, statisticians, bio-informaticians and biologists.
SMILE is affiliated to the Stochastics and Biology group of LPSM (Lab of Probability, Statistics and Modeling) at Sorbonne Université (ex Université Pierre et Marie Curie Paris 06).
SMILE is hosted within the CIRB (Center for Interdisciplinary Research in Biology) at Collège de France.
SMILE is supported by Collège de France and CNRS.
Visit also our homepage at CIRB.

Recent contributions of the SMILE group related to SARS-Cov2 and COVID-19.

Directions

SMILE is hosted at Collège de France in the Latin Quarter of Paris. To reach us, go to 11 place Marcelin Berthelot (stations Luxembourg or Saint-Michel on RER B).
Our working spaces are rooms 107, 121 and 122 on first floor of building B1 (ask us for the code). Building B1 is facing you upon exiting the traversing hall behind Champollion's statue.

Contact

You can reach us by email (amaury.lambert - at - upmc.fr) or (smile - at - listes.upmc.fr).

Light on

Publication

2015

Time Reversal Dualities for some Random Forests

We consider a random forest \$$\mathcal{F}^*\$$, defined as a sequence of i.i.d. birth-death (BD) trees, each started at time 0 from a single ancestor, stopped at the first tree having survived up to a fixed time \$$T\$$. We denote by \$$\left(\xi^*_t, 0\leq t \leq T \right)\$$ the population size process associated to this forest, and we prove that if the BD trees are supercritical, then the time-reversed process \$$\left(\xi^*_{T-t}, 0 \leq t \leq T\right)\$$, has the same distribution as \$$\left(\widetilde\xi^*_t, 0 \leq t \leq T\right)\$$, the corresponding population size process of an equally defined forest \$$\widetilde{\mathcal{F}}^*\$$, but where the underlying BD trees are subcritical, obtained by swapping birth and death rates or equivalently, conditioning on ultimate extinction. We generalize this result to splitting trees (i.e. life durations of individuals are not necessarily exponential), provided that the i.i.d. lifetimes of the ancestors have a specific explicit distribution, different from that of their descendants. The results are based on an identity between the contour of these random forests truncated up to \$$T\$$ and the duality property of L\'evy processes. This identity allows us to also derive other useful properties such as the distribution of the population size process conditional on the reconstructed tree of individuals alive at \$$T\$$, which has potential applications in epidemiology.

Publication

2020

Predicted success of prophylactic antiviral therapy to block or delay SARS-CoV-2 infection depends on the targeted mechanism

Repurposed drugs that are immediately available and have a good safety profile constitute a first line of defense against new viral infections. Despite a limited antiviral activity against SARS-CoV-2, several drugs serve as candidates for application, not only in infected individuals but also as prophylaxis to prevent infection establishment. Here we use a stochastic model to describe the early phase of a viral infection. We find that the critical efficacy needed to block viral establishment is typically above 80\%. This value can be improved by combination therapy. Below the critical efficacy, establishment can still sometimes be prevented; for that purpose, drugs blocking viral entry into target cells (or equivalently enhancing viral clearance) are more effective than drugs reducing viral production or enhancing infected cell death. When a viral infection cannot be prevented because of high exposure or low drug efficacy, antivirals can still delay the time to reach detectable viral loads from 4 days when untreated to up to 30 days. This delay flattens the within-host epidemic curve, and possibly reduces transmission and symptom severity. These results suggest that antiviral prophylaxis, even with reduced efficacy, could be efficiently used to prevent or alleviate infection in people at high risk. It could thus be an important component of the strategy to combat the SARS-CoV-2 pandemic in the months or years to come.

Upcoming seminars

Resources

Planning des salles du Collège de France.
Intranet du Collège de France.